双材料基本解弹塑性边界元法

提出并研究采用双材料基本解的弹塑性边界元法,得到了内点应力公式中有关奇点塑性应变自由项的完整表达式,并利用非连续边界单元和非连续区域单元解决了当奇点位于界面上时该自由项难于确定,以及计算区域Cauchy主值积分的常塑性应变场法在与界面相连的奇异区域单元上无法实施的困难．采用双材料基本解的弹塑性边界无法针对双材料的结构特点,特别适于分析有关弹塑性双材料界面及界面裂纹问题．     

有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响

随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视。界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性。因此双材料界面附近的力学分析是比较复杂的。本文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响。运用弹性力学中的 Goursat 公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数。通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子。计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定。分析结果可以为预测双材料结构复合材料界面失效位置提供参考。     

一种确定结合材料界面端应力强度因子的数值方法

基于弹性力平面问题的基本方程，给出了结合材料界面端的应力奇异性特征方程以及位移场和奇异应力场。提出了一种确定结合材料界面端应力强度因子的数值外插方法。对界面端区域进行了有限元网格单元划分。经过具体实例检验进一步确定了求解应力强度因子的最佳方向，该数值外插法的计算结果精度符合工程应用的要求，为工程材料强度的评价提供了有效的计算途径。     

界面上应力波传播规律的动态光弹性试验研究

采用动态光弹性方法,对应力波在杆-杆和板-板双材料连接界面上的反射和透射传播规律展开研究．通过对双材料粘接模型施加冲击载荷作用,采集和分析等差线条纹,计算出最大剪应力值．对于两种试验模型应力波在界面上都以透射为主,对应力波的阻隔作用不明显,这与接触式界面对应力波有较强的阻隔作用有较大区别,在应用界面减弱应力波的作用时应注意区分．试验结果与理论计算结果基本保持一致,并由此证明采用动态光弹性法研究应力波在界面上传播规律的可行性．     

双材料界面应力分析的局部杂交法

本文用云纹干涉法测取双材料高梁受集中载荷时沿ｘ，ｙ轴的位移场ｕ，ｖ．以其作为界面局部微区的边界条件，用有限元计算此微区内界面上的应力分量．与光弹性及全梁有限元法比较，发现局部杂交法的精度最高．     

光弹法实测正交异性双材料界面裂纹断裂参数

采用光弹贴片法实测正交异性双材料界面裂纹尖端区域的应力应变场, 进而求出界面裂纹的断裂力学参量. 将正交异性双材料板加工成拉伸试件,在聚碳酸酯贴片 的单侧表面镀金属铝膜,以提高贴片的反射效率. 沿贴片后的双材料界面预制裂缝,逐渐加 大载荷,得到一系列清晰的等差线条纹图. 利用正交异性双材料界面裂纹尖端应力分量表达 式计算出应力强度因子. 实验表明,光弹贴片法可有效地分析正交异性双材料界面裂纹问题.     

双材料梁界面力学及其应用:综述

双材料结构在工程中得到了广泛应用,如薄膜涂层、压电材料、复合材料层合板和夹层板、粘结接头、FRP加固混凝土结构等;然而,这些结构的破坏通常是从界面及其附近开始的.通常利用损伤力学的方法(材料强度的方法)来预测裂纹的萌生,利用断裂力学的方法来预测裂纹的扩展;因此,开展双材料结构的界面应力分析和具分层双材料结构的断裂以及相关分析是至关重要的.首先介绍双材料梁粘结界面应力分析的基本模型,从而为预测裂纹的萌生提供了有力工具.然后综述双材料梁界面断裂力学分析的基本方法,并详细介绍解析解求解的裂纹尖端法及其相关模型,重点强调裂纹尖端变形对分析结果的影响.最后介绍界面分层对双材料结构其它力学特性的影响,例如屈曲和振动特性.     

双层金属纳米板界面能密度的尺寸效应

界面能密度是表征纳米复合材料与结构界面力学性质的重要物理量.采用分子动力学方法计算了不同面心立方金属晶体构成的双材料纳米薄板结构的界面能密度,分析了界面晶格结构形貌变化及界面效应对原子势能的影响.结果表明:双材料纳米薄板界面具有周期性褶皱状疏密相间的晶格结构形貌,界面上原子势能亦呈现周期性分布特性,而靠近界面的两侧原子势能与板内原子势能具有明显差异.拉格朗日界面能密度和欧拉界面能密度均随双层薄板厚度的增加而增加,最终趋向于块体双材料结构的界面能密度.     

双材料界面裂纹复应力强度因子的正则化边界元法

双材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性, 许多用于表征经典平方根($r^{1/2})$和负平方根($r^{-1/2})$渐近物理场的传统数值方法失效, 给界面裂纹复应力强度因子($K_{1} +{i}K_{2} )$的精确求解增加了难度. 引入一种含有复振荡因子的新型"特殊裂尖单元", 可精确表征裂纹尖端渐近位移和应力场的振荡特性, 在避免裂尖区域高密度网格剖分的情况下, 可实现双材料界面裂纹复应力强度因子的精确求解. 此外, 结合边界元法中计算近奇异积分的正则化算法, 成功求解了大尺寸比(超薄)双材料界面裂纹的断裂力学参数. 数值算例表明, 所提算法稳定, 效率高, 在不增加计算量的前提下, 显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性.      

自适应网格技术在流体力学界面处理中的应用

自适应网格技术是流体力学数值计算中的重要内容之一．不仅能够处理大变形问题，而且能够大大提高物质界面的计算精度。针对结构网格给出了网格细化结构、误差估计、数据管理、网格产生算法等。通过对强激波双马赫反射及Rayleigh-Taylor界面不稳定性现象进行数值模拟．获得符合精度要求的对激波阵面及物质界面自适应跟踪结果。     

Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method

The transient response of finite bimaterial plates with interface cracks is analyzed directly in the time domain by using the scaled boundary finite-element method. A bimaterial plate is divided into a few subdomains. Only the boundaries of the subdomains are discretized with line elements leading to great flexibility in mesh generation. The displacement and stress fields are expressed as a series solution which separates the singular stress term from other high-order terms. The oscillatory stress singularity in the radial direction emanating from the scaling center is represented analytically. The complex dynamic stress intensity factors are evaluated directly from either the stresses or the crack opening displacements of the singular stress term. Numerical examples of cracked anisotropic bimaterial plates are presented to verify the accuracy of the present technique and to provide additions to the very limited number of reference solutions in the literature.     

Analysis of a mode-I crack perpendicular to an imperfect interface

The elastostatic problem of a mode-I crack embedded in a bimaterial with an imperfect interface is investigated. The crack is in proximity to and perpendicular to the imperfect interface, which is governed by linear spring-like relations. The Fourier transform is applied to reduce the associated mixed-boundary value problem to a singular integral equation with Cauchy kernel. By numerically solving the resulting equation, stress intensity factors near both crack tips are evaluated. Obtained results reveal that the stress intensity factors in the presence of the imperfect interface vary between that with a perfect interface and that with a completely debonding interface. Moreover, an increase in the interface parameters decreases the stress intensity factors. In particular, when crack approaches to the weakened interface closer, the stress intensity factors become larger for a sliding interface, and become larger or smaller for a Winkler interface, depending on the crack lying in a stiffer or softer material. The influences of the imperfection of the interface on the stress intensity factors for a bimaterial composed of aluminum and steel are presented graphically.     

折线裂纹和两相材料界面的相互作用

利用螺位错基本解建立了和界面相交的折线裂纹的Cauchy型积分方程，根据奇异积分方程理论，得出了确定折线裂纹和界面交点处的奇性应力指数的特征方程，以及交点处各角形域内的奇性应力，利用所得的交点处的奇性应力定义了折线裂纹和界面交点处的应力强度因子，对所得积分方程进行数值求解，可得裂纹端点以及裂纹和界面交点处的应力强度因子。     

垂直于界面V型缺口尖端的应力奇异性及其应用

基于双材料垂直于界面V型缺口理论,给出了单一材料和双材料裂纹问题、V型缺口问题应力强度因子的统一定义,得到了应力外推法计算双材料K_I的公式,数值算例验证了本文方法的有效性.以双材料单向拉伸和三点弯曲模型为对象,深入研究了双材料中弹性模量、泊松比、缺口深度、缺口张角对缺口尖端奇异应力场的影响,获得了一定范围内各种参数变化对缺口尖端奇异应力场的影响规律,为异体材料形成的V型缺口在应力断料中的应用提供了必要的参考依据.     

Numerical solutions of singular integral equations for planar rectangular interfacial crack in three dimensional bimaterials

Stress intensity factors for a three dimensional rectangular interfacial crack were considered using the body force method. In the numerical calculations, unknown body force densities were approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack exactly. The calculation shows that the numerical results are satisfied. The stress intensity factors for a rectangular interface crack were indicated accurately with the varying aspect ratio, and bimaterial parameter.     

Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

Stress intensity factor for a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation

The asymptotic problem of a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation is investigated. The linear transformation method for the problem of the anisotropic bimaterial with a straight interface is proposed. The stress intensity factor for the kinked interfacial crack in the anisotropic composite is obtained from the solution of the transformed problem of the kinked interfacial crack in the isotropic bimaterial based on the linear transformation method. The effects of the material parameters as well as the kink angle on the stress intensity factor are discussed from numerical results of the stress intensity factor. The finite element analysis is carried out to verify the stress intensity factor obtained by using the linear transformation. The influence of the material orientations on the stress intensity factor is investigated for the kinked crack in the bimaterial consisting of dissimilar inclined orthotropic materials.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。